Question

I got 300 cubic cm but the answer is 308 on the answer sheet. How?

Answer 1

Check below

Explanation:

Writing the equation using the first sentence, we get

`V=kT/P`, where `k` is a constant of proportionality.

Now, let's use the first set of values.

`231 cm^3=k*(300K)/(20(lb)/(cm^2))`

`k=((231 cm^3) * (20(lb)/(cm^2)))/(300K)`

`k=15.4 (lb*cm)/(K)`

Now, let's use the second set of values and the constant determined above.

`V=15.4(lb*cm)/(K)*(320K)/(16(lb)/(cm^2))`

`V=308 cm^3`

You may have rounded the `15.4` to `15` as an intermediate step. This is something I would refrain from doing; always round at the end of a question.

Another potential reason is that the values in the question to only have `1` significant digit. Thus, `308` would round to `300`.

In either case, I think you got the idea behind the question, so you should be fine.

Answer 2

Yes answer is `308cm^3`. For details see below.

Explanation:

As volume `V` of a given mass of gas varies directly as temperature `T` and inversely as pressure `P`, the relation between two states of the same mass of gas is

`(P_1V_1)/(T_1)=(P_2V_2)/(T_2)`

Here `P_1=20(lb)/(cm)^2`, `V_1=231cm^3` and `T_1=300^@K`

and `P_2=16(lb)/(cm)^2` and `T_2=320^@K`

Hence `(20xx231)/300=(16xxV_2)/320`

and `V_2=(20xx231)/300xx320/16`

= `(20xx231)/300xxcancel320^20/cancel16^1`

= `(20xx231)/300xx20`

= `(20xx231)/cancel300^15xxcancel20^1`

= `(20xx231)/15=(20xx231)/(5xx3)`

= `(cancel20^4xxcancel231^77)/(cancel5^1xxcancel3^1)`

= `4xx77=308`